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   <div id="projectname">Parallel Gaussian Process Regression
   &#160;<span id="projectnumber">1.0.0</span>
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   <div id="projectbrief">The implementation of parallel Gaussian process (GP) regression is based on the following publication: Jie Chen, Nannan Cao, Kian Hsiang Low, Ruofei Ouyang, Colin Keng-Yan Tan &amp; Patrick Jaillet. Parallel Gaussian Process Regression with Low-Rank Covariance Matrix Approximations. In Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence (UAI 2013), Bellevue, WA, Jul 11-15, 2013.</div>
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<a href="pgpr__fgp_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;</div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="preprocessor">#ifndef _PGPR_FGP_H_</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="preprocessor">#define _PGPR_FGP_H_</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="pgpr__util_8h.html">pgpr_util.h</a>&quot;</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="pgpr__cov_8h.html">pgpr_cov.h</a>&quot;</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="pgpr__chol_8h.html">pgpr_chol.h</a>&quot;</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"><a class="line" href="classpgpr__fgp.html">   12</a></span>&#160;<span class="keyword">class </span><a class="code" href="classpgpr__fgp.html">pgpr_fgp</a></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;{</div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="keyword">private</span>:</div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;  <a class="code" href="classpgpr__cov.html">pgpr_cov</a> *cov;</div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;  Doub h_mu;</div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;  <a class="code" href="classpgpr__vector.html">Vdoub</a> pmu;</div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;  <a class="code" href="classpgpr__vector.html">Vdoub</a> pvar;</div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;  Doub elapsed;</div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;  Doub rmse;</div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;  Doub mnlp;</div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;</div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;  <span class="keyword">inline</span> <a class="code" href="classpgpr__chol.html">pgpr_chol</a> *chol_cov(<a class="code" href="classpgpr__matrix.html">Mdoub</a> K_dd) {</div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;    <a class="code" href="classpgpr__chol.html">pgpr_chol</a> *chol = <span class="keyword">new</span> <a class="code" href="classpgpr__chol.html">pgpr_chol</a>(K_dd);</div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;    <span class="keywordflow">return</span> chol;</div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;  }</div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;</div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="keyword">public</span>:</div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;  <span class="comment">//full gp regression</span></div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;  Int full_reg(<a class="code" href="classpgpr__matrix.html">Mdoub</a> obs, Int dnum, <a class="code" href="classpgpr__matrix.html">Mdoub</a> xt, Int ts, <a class="code" href="classpgpr__vector.html">Vdoub</a> &amp;t_mu, <a class="code" href="classpgpr__vector.html">Vdoub</a> &amp;t_var) {</div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;    <span class="comment">//step 1:cholesky decomposition</span></div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;    Int ss = dnum;</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;    <a class="code" href="classpgpr__vector.html">Vdoub</a> v(ss);</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;    <a class="code" href="classpgpr__vector.html">Vdoub</a> alpha(ss);</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;    <span class="comment">//Vdoub beta(ss);</span></div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;    <a class="code" href="classpgpr__matrix.html">Mdoub</a> K_dd;</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;    <span class="comment">//build K+\sigma^2_n I.</span></div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;    cov-&gt;se_ard_n(obs, ss, K_dd);</div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;    <a class="code" href="classpgpr__chol.html">pgpr_chol</a> *chol = chol_cov(K_dd);</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;    <span class="comment">//step 2: compute alpha</span></div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;    <span class="keywordflow">for</span>(Int i = 0; i &lt; ss; i++) {</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;      v[i] = obs[i][cov-&gt;<a class="code" href="classpgpr__cov.html#ab24ca5303c1a5e6865109a8e1ba32f0f">dim</a>] - h_mu;</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;    }</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;    chol-&gt;<a class="code" href="classpgpr__chol.html#a567b23e2e93a85675de26550d5e4cb38">solve</a>(v, alpha);</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;    <span class="comment">//step 3: predictive mean</span></div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;    <span class="comment">//Int ts = xt.nrows();</span></div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;    t_mu.resize(ts);</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;    t_var.resize(ts);</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;    <a class="code" href="classpgpr__matrix.html">Mdoub</a> K_td;</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;    cov-&gt;se_ard(xt, ts, obs, ss, K_td);</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;    <span class="comment">// \bar{f}_*</span></div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;    <span class="keywordflow">for</span>(Int i = 0; i &lt; ts; i++) {</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;      t_mu[i] = h_mu;</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;      <span class="keywordflow">for</span>(Int j = 0; j &lt; ss; j++) {</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;        t_mu[i] += K_td[i][j] * alpha[j];</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;      }</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;      <span class="comment">//Step:4 predictive variance</span></div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;      <span class="comment">//k_{i,i}</span></div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;      t_var[i] = cov-&gt;se_ard_n(xt[i], xt[i]);</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;      <span class="comment">//k_{*f}</span></div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;      <a class="code" href="classpgpr__vector.html">Vdoub</a> K_ti(ss);</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;      <span class="keywordflow">for</span>(Int j = 0; j &lt; ss; j++) {</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;        K_ti[j] = K_td[i][j];</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;      }</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;      <span class="comment">//var[f_ii]</span></div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;      <span class="comment">//v[i]=L\k*[i]</span></div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;      chol-&gt;<a class="code" href="classpgpr__chol.html#a365839254c16b047b2e36a7937b8593f">elsolve</a>(K_ti, v);</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;      <span class="comment">//predictive variance</span></div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;      <span class="keywordflow">for</span>(Int j = 0; j &lt; ss; j++) {</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;        t_var[i] -= v[j] * v[j];</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;      }</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;    }</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;    <span class="keyword">delete</span> chol;</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;    <span class="keywordflow">return</span> SUCC;</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;  }</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;  <a class="code" href="classpgpr__fgp.html">pgpr_fgp</a>(<a class="code" href="classpgpr__vector.html">Vdoub</a> h, Int dx) {</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;    cov = <span class="keyword">new</span> <a class="code" href="classpgpr__cov.html">pgpr_cov</a>(h, dx);</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;    h_mu = h[h.size() - 1];</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;  }</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;  <a class="code" href="classpgpr__fgp.html">pgpr_fgp</a>(Char * hypf) {</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;    cov = <span class="keyword">new</span> <a class="code" href="classpgpr__cov.html">pgpr_cov</a>(hypf);</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;    h_mu = cov-&gt;<a class="code" href="classpgpr__cov.html#ad57517c36c587894616f19bd02025747">mu</a>;</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;  }</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;  ~<a class="code" href="classpgpr__fgp.html">pgpr_fgp</a>() {</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;    <span class="keyword">delete</span> cov;</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;  }</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;  Int regress(Char * train, Char * test) {</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;    Int ddim = cov-&gt;<a class="code" href="classpgpr__cov.html#ab24ca5303c1a5e6865109a8e1ba32f0f">dim</a> + 1;</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;    <a class="code" href="classpgpr__matrix.html">Mdoub</a> traindata(1, ddim);</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;    <a class="code" href="classpgpr__matrix.html">Mdoub</a> testset(1, ddim);</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;    Int ds = loadData(train, traindata);</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;    Int ts = loadData(test, testset);</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;    pmu.resize(ts);</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;    pvar.resize(ts);</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;    <a class="code" href="classpgpr__timer.html">pgpr_timer</a> timer;</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;    timer.<a class="code" href="classpgpr__timer.html#ae30d8bfbf046764791f934d198f122b3">start</a>();</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;    full_reg(traindata, ds, testset, ts, pmu, pvar);</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;    elapsed = timer.<a class="code" href="classpgpr__timer.html#ac81e09244717a72ce57242e86aa6c200">end</a>();</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;    <a class="code" href="classpgpr__vector.html">Vdoub</a> trueval(ts);</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;    <span class="keywordflow">for</span>(Int i = 0; i &lt; ts; i++) {</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;      trueval[i] = testset[i][ddim - 1];</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;    }</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;    rmse = getRmse(trueval, pmu);</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;    mnlp = getMnlp(trueval, pmu, pvar);</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;    <span class="keywordflow">return</span> SUCC;</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;  }</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;  <span class="keywordtype">void</span> outputRst(Char * output) {</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;    FILE * fp;</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;    Int ts = pmu.size();</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;    fp = fopen(output, <span class="stringliteral">&quot;w&quot;</span>);</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;    <span class="keywordflow">if</span>(fp == NULL) {</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;      <span class="keywordflow">throw</span>(<span class="stringliteral">&quot;Fail to open file\n&quot;</span>);</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;    }</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;    <span class="keywordflow">for</span>(Int i = 0; i &lt; ts; i++) {</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;      fprintf(fp, <span class="stringliteral">&quot;%.4f %.4f\n&quot;</span>, pmu[i], pvar[i]);</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;    }</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;    pmsg(LEV_PRG, stdout, <span class="stringliteral">&quot; %.4f | %.4f | %.4f |\n&quot;</span>, elapsed, rmse, mnlp);</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;    fclose(fp);</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;  }</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;};</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="ttc" id="pgpr__chol_8h_html"><div class="ttname"><a href="pgpr__chol_8h.html">pgpr_chol.h</a></div><div class="ttdoc">This file provides Cholesky factorization and some related useful functions such as inverse...</div></div>
<div class="ttc" id="classpgpr__timer_html_ac81e09244717a72ce57242e86aa6c200"><div class="ttname"><a href="classpgpr__timer.html#ac81e09244717a72ce57242e86aa6c200">pgpr_timer::end</a></div><div class="ttdeci">Doub end()</div><div class="ttdoc">Stop a timer and compute the elapsed time in seconds. </div><div class="ttdef"><b>Definition:</b> pgpr_util.h:732</div></div>
<div class="ttc" id="classpgpr__chol_html_a567b23e2e93a85675de26550d5e4cb38"><div class="ttname"><a href="classpgpr__chol.html#a567b23e2e93a85675de26550d5e4cb38">pgpr_chol::solve</a></div><div class="ttdeci">void solve(Vdoub &amp;b, Vdoub &amp;x)</div><div class="ttdoc">Solving A* x = b using back substitution. </div><div class="ttdef"><b>Definition:</b> pgpr_chol.h:52</div></div>
<div class="ttc" id="classpgpr__chol_html"><div class="ttname"><a href="classpgpr__chol.html">pgpr_chol</a></div><div class="ttdoc">This class provides Cholesky factorization and some related useful functions such as inverse...</div><div class="ttdef"><b>Definition:</b> pgpr_chol.h:14</div></div>
<div class="ttc" id="classpgpr__timer_html_ae30d8bfbf046764791f934d198f122b3"><div class="ttname"><a href="classpgpr__timer.html#ae30d8bfbf046764791f934d198f122b3">pgpr_timer::start</a></div><div class="ttdeci">void start()</div><div class="ttdoc">Start a timer. </div><div class="ttdef"><b>Definition:</b> pgpr_util.h:715</div></div>
<div class="ttc" id="classpgpr__cov_html_ab24ca5303c1a5e6865109a8e1ba32f0f"><div class="ttname"><a href="classpgpr__cov.html#ab24ca5303c1a5e6865109a8e1ba32f0f">pgpr_cov::dim</a></div><div class="ttdeci">Int dim</div><div class="ttdef"><b>Definition:</b> pgpr_cov.h:19</div></div>
<div class="ttc" id="classpgpr__vector_html"><div class="ttname"><a href="classpgpr__vector.html">pgpr_vector&lt; Doub &gt;</a></div></div>
<div class="ttc" id="pgpr__util_8h_html"><div class="ttname"><a href="pgpr__util_8h.html">pgpr_util.h</a></div><div class="ttdoc">This file contains a collection of useful functions such as macro-like inline functions, debug functions, exception handling, file I/O, and a real-time timer class. </div></div>
<div class="ttc" id="classpgpr__fgp_html"><div class="ttname"><a href="classpgpr__fgp.html">pgpr_fgp</a></div><div class="ttdoc">This class provides basic regression function using full GP. </div><div class="ttdef"><b>Definition:</b> pgpr_fgp.h:12</div></div>
<div class="ttc" id="classpgpr__cov_html_ad57517c36c587894616f19bd02025747"><div class="ttname"><a href="classpgpr__cov.html#ad57517c36c587894616f19bd02025747">pgpr_cov::mu</a></div><div class="ttdeci">Doub mu</div><div class="ttdef"><b>Definition:</b> pgpr_cov.h:18</div></div>
<div class="ttc" id="pgpr__cov_8h_html"><div class="ttname"><a href="pgpr__cov_8h.html">pgpr_cov.h</a></div><div class="ttdoc">This file provides the covariance class: pgpr_cov, which compute the covariance matrix. </div></div>
<div class="ttc" id="classpgpr__matrix_html"><div class="ttname"><a href="classpgpr__matrix.html">pgpr_matrix&lt; Doub &gt;</a></div></div>
<div class="ttc" id="classpgpr__timer_html"><div class="ttname"><a href="classpgpr__timer.html">pgpr_timer</a></div><div class="ttdoc">This timer class can provide real-time measure (in seconds) incurred by a block of running program...</div><div class="ttdef"><b>Definition:</b> pgpr_util.h:702</div></div>
<div class="ttc" id="classpgpr__chol_html_a365839254c16b047b2e36a7937b8593f"><div class="ttname"><a href="classpgpr__chol.html#a365839254c16b047b2e36a7937b8593f">pgpr_chol::elsolve</a></div><div class="ttdeci">void elsolve(Vdoub &amp;b, Vdoub &amp;y)</div><div class="ttdoc">solving el * y = b using back substitution. </div><div class="ttdef"><b>Definition:</b> pgpr_chol.h:78</div></div>
<div class="ttc" id="classpgpr__cov_html"><div class="ttname"><a href="classpgpr__cov.html">pgpr_cov</a></div><div class="ttdoc">The pgpr_cov class provides the informaiton of covariance. </div><div class="ttdef"><b>Definition:</b> pgpr_cov.h:12</div></div>
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